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HKIMO 2026 Grade 7 National Preliminary Set 02

Question 1

A farm has chickens and rabbits. The number of chickens is four times the number of rabbits. They have 360 legs altogether. How many chickens are there?
  1. 30
  2. 60
  3. 90
  4. 120

Question 2

The distance between Hanoi and Bangkok is 988 km. A plane takes off from Hanoi at 12:30 and flies to Bangkok at 760 km/h. At what time does it land?
  1. 15:10
  2. 13:48
  3. 13:30
  4. 13:18

Question 3

According to the pattern, find the tenth term of $1,3,7,15,31,63,\ldots$.
  1. 127
  2. 255
  3. 511
  4. 1023

Question 4

A box contains 100 blue, 100 yellow and 100 purple balls. What is the least number Lam must draw at random to guarantee nine balls of one colour?
  1. 25
  2. 30
  3. 10
  4. 27

Question 5

The two-digit number $\overline{AB}$ is prime and $A\times B=12$. What is the difference between $A$ and $B$?
  1. 1
  2. 4
  3. 5
  4. 8

Question 6

How many integer values of $x$ satisfy $-22\le7x-1<69$?
  1. 12
  2. 13
  3. 14
  4. 15

Question 7

Given $A:B=4:3$, $B:C=9:7$ and $A+B-C=56$, find $A$.
  1. 48
  2. 16
  3. 12
  4. 38

Question 8

Convert $1.484848\ldots$ to a fraction in lowest terms.
  1. $\frac{147}{99}$
  2. $\frac{148}{100}$
  3. $\frac{49}{33}$
  4. $\frac{49}{99}$

Question 9

Find $3+6+12+24+\cdots+384+768$.
  1. 1335
  2. 1533
  3. 1500
  4. 3500

Question 10

The sum of six consecutive even numbers is 258. Find the largest of them.
  1. 48
  2. 46
  3. 38
  4. 50

Question 11

Find the units digit of $2^{2020}\times4^{2021}\times6^{2022}$.
  1. 2
  2. 4
  3. 6
  4. 8

Question 12

How many three-digit numbers are divisible by 3 but not by 4?
  1. 360
  2. 270
  3. 225
  4. 252

Question 13

The eight-digit number $\overline{1710A22B}$ is divisible by 12. Find the greatest value of $A\times B$.
  1. 28
  2. 60
  3. 72
  4. 90

Question 14

Find the number of positive factors of 720.
  1. 30
  2. 42
  3. 18
  4. 26

Question 15

Given $A=10\times11\times12\times\cdots\times49\times50$, how many zeros end $A$?
  1. 8
  2. 5
  3. 9
  4. 11

Question 16

Find the sum of all interior angles of a regular pentagon.
  1. $360^\circ$
  2. $180^\circ$
  3. $540^\circ$
  4. $720^\circ$

Question 17

Uncle An has a rectangular garden 9 m wide and 10 m long. He uses a corner for a pond as shown and grows vegetables in the rest. Find the vegetable area in $\mathrm{m}^2$. Take $\pi=22/7$.

Editorial interpretation of the drawing: the pond is a quarter-circle centered at the upper-left corner.

Question illustration
  1. 51.5
  2. 38.5
  3. 60
  4. 46.5

Question 18

A metal cuboid measuring 12 cm by 8 cm by 18 cm is melted and recast as a cube. Find the cube’s total surface area in $\mathrm{cm}^2$.
  1. 1728
  2. 576
  3. 144
  4. 864

Question 19

A rope is bent into a square of side 22. If the same rope is bent into a circle, find its radius. Take $\pi=22/7$.
  1. 17
  2. 14
  3. 28
  4. 7

Question 20

A square tile of side 20 cm has the pattern below, with four identical right-angled triangles and a small shaded square. Find the shaded area in $\mathrm{cm}^2$.

Question illustration
  1. 40
  2. 60
  3. 80
  4. 20